Bézier curve


last updated: 20050118 
Given a set of n+1 control points P_{i} the Bézier curve is
written in terms of Bernstein polynomials:
The curve has the following properties:
 there is no line that has more intersections with a Bézier curve than
with the curve composed by the line segments through the points.
 the curve can be translated and rotated by performing these operations on
the control points.
 a numerical instability for large numbers of control points.
 moving a single control point changes the global shape of the curve.
This can be avoided by smoothly patching together loworder Bézier curves.
The rational Bézier curve is a generalization of the curve: xxx
Another generalization of the curve is the Bspline. 